Operation Research

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CAREER POINT
UNIVERSITY
KOTA (Raj.)
“BUSINESS APPLICATIONS OF
OPERATION RESEARCH”
OPERATION RESEARCH
Submitted To- Submitted By-
Mr. Ankush Paliwal Sir Surbhi Hada (K13239)
(Asst. Prof. of School Barkha Daswani (K13517)
Of Commerce and MGMT) Ravi Singh (K 13389)
Ashim Roy (K13226)

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ACKNOLODGEMENT
We would like to express our special thanks of gratitude to our teacher Mr.
Ankush Paliwal Sir as well as our HOD Mr. Ashish Suri Sir who gave us the golden
opportunity to do this wonderful project on the topic “Business Application of
Operation Research”, which also helped us in doing a lot of Research and we came to
know about so many new things. We are really thankful to them. Secondly we would
also like to thank our parents and friends who helped us a lot in finishing this project
within the limited time.
We are also making this Assignment not only for marks but also to increase our
knowledge.
THANKS AGAIN TO ALL WHO HELPED US.

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CONTEXT:
 Abstract PG. 04
 Introduction PG.05
 Overview PG.06
 Early History PG. 07
 Applications of Operation Research PG. 08
 OR Application in Business PG. 10
 Phases of Operation Research Study PG. 12
 Features of Operation Research PG. 14
 Scopeof Operation Research PG. 15
 Simplification of OR Model PG. 17
 Limitations of Operation Research PG. 18
 Conclusion PG. 19
 Bibliography PG. 19

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 Abstract:
Operations Research is a bouquet of mathematical techniques that have evolved over the last
six decades to improve the process of business decision making. Operations Research offers tools to
optimize and find the best solutions to myriad decisions that managers have to take in their day to day
operations or while carrying out strategic planning. Today, with the advent of operations research
software, these tools can be applied by managers even without any knowledge of the mathematical
techniques that underlie the solution procedures. To find the reasons for the attractiveness of general
business problems to OR researchers, the main type of business decision making problems amenable
to OR are identified, and some of the many problems solved by using OR are techniques. While
mathematical programming is the most widely applied technique, linear programming, transportation,
assignment and simulation methods are increasingly widely used. OR now plays an important role in
the operation of business problem solving and this importance is likely to increase, creating the
opportunity for OR to play an even greater role.

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 Introduction:
Operations Research (or Management Science or Decision Sciences) is a scientific manner of
decision making, mostly under the pressure of scarce resources. The objective of decision making is
often the maximization of profit, minimization of cost, better efficiency, better operational or tactical
or strategic planning or scheduling, better pricing, better productivity, better throughput, better
location, better risk management, or better customer service. The scientific manner involves extensive
use of mathematical representations or models of real life situations. These representations allow
employment of mathematical techniques to arrive at optimal or near optimal decisions after
consideration of all possible options.
Since the advent of the industrial revolution, the world has seen a remarkable growth in the size
and complexity of business organizations. An integral part of this revolutionary change has been a
tremendous increase in the division of labour and segmentation of management responsibilities in
these organizations. The results have been spectacular. However, along with its blessings, this
increasing specialization has created new problems, problems that are still occurring in many
organizations. One problem is a tendency for the many components of an organization to grow into
relatively autonomous empires with their own goals and value systems, thereby losing sight of how
their activities and objectives mesh with those of the overall organization. What is best for one
component frequently is detrimental to another, so the components may end up working at cross
purposes. A related problem is that as the complexity and specialization in an organization increase, it
becomes more and more difficult to allocate the available resources to the various activities in a way
that is most effective for the organization as a whole. These kinds of problems and the need to find a
better way to solve them provided the environment for the emergence of operations research.
The roots of OR can be traced back many decades, when early attempts were made to use a
scientific approach in the management of organizations. However, the beginning of the activity called
operations research has generally been attributed to the military services early in World War II.
Because of the war effort, there was an urgent need to allocate scarce resources to the various military
operations and to the activities within each operation in an effective manner. Therefore, the British and
then the U.S. military management called upon a large number of scientists to apply a scientific
approach to dealing with this and other strategic and tactical problems. In effect, they were asked to do
research on (military) operations. These teams of scientists were the first OR teams. By developing
effective methods of using the new tool of radar, these teams were instrumental in winning the Air
Battle of Britain.

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 Overview:
Operational research (OR) encompasses a wide range of problem-solving techniques and methods
applied in the pursuit of improved decision-making and efficiency, such as simulation, mathematical
optimization, queueing theory and other stochastic-process models, Markov decision processes,
econometric methods, data envelopment analysis, neural networks, expert systems, decision analysis,
and the analytic hierarchy process. Nearly all of these techniques involve the construction of
mathematical models that attempt to describe the system. Because of the computational and statistical
nature of most of these fields, OR also has strong ties to computer science and analytics. Operational
researchers faced with a new problem must determine which of these techniques are most appropriate
given the nature of the system, the goals for improvement, and constraints on time and computing
power.
The major sub disciplines in modern operational research, as identified by the journal Operations
Research, are:
 Computing and information technologies
 Financial engineering
 Manufacturing, service sciences, and supply chain management
 Policy modelling and public sector work
 Revenue management
 Simulation
 Stochastic models
 Transportation

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 Early History:
Operations Research had its origins in the Second World War when a group of scientists and
engineers was formed to aid the military in proper radar deployment, convoy management, anti-
submarine operations, and mining operations. The development of the linear programming solution
methodology by George Dantzig and the advent of computers in the early 1950s led to enormous
interest in operation research applications in business. Industries set up operations research groups
especially in areas relating to oil refineries and finance. Simultaneously, other methodologies such as
integer programming solution methodology, queuing theory, graph and network theory, non-linear
programming, stochastic programming, game theory, dynamic programming, Markov decision
processes, meta-heuristic procedures such as simulated annealing, genetic and tabu search, neural
networks, multi-criteria or multi-objective analysis, analytic hierarchy process, simulation, and Petri
nets were being developed to tackle business problems.
The advent of computers with large memories and high speeds in the 1990s led to the second major
wave of interest in operations research. The major areas where operations research was applied in the
second wave were yield or revenue management, crew management and network design in the airlines
sector, and finance and supply chain management. Today, the opportunities of exploiting operations
research techniques have multiplied manifold with the huge amount of data available through ERP,
CRM, or point of sale capture for analysis and decision making.

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 Applications of Operation Research:
The breadth of applications of operations research in business can be gauged from a reading of the
annual Franz Edelman competition winners’ accomplishments, few of which are listed below:
 2013: Dutch Delta Program Commissioner used mixed integer nonlinear programming to
derive an optimal investment strategy for strengthening dikes for protection against high water
and keeping freshwater supplies up to standard, resulting in savings of €8 billion in investment
costs.
 2012: TNT Express developed a portfolio of multi-commodity and vehicle routing models for
package and vehicle routing and scheduling, planning of pickup and delivery, and supply chain
optimization for its operations across 200 countries using 2,600 facilities, 30,000 road vehicles,
and 50 aircraft resulting, in savings of €207 million over the period 2008–2011 and reduction
in CO2 emissions by 283 million kilograms.
 2011: Midwest Independent Transmission System Operator used mixed integer programming
to determine when each power plant should be on or off, the power plant output levels and
prices to minimize the cost of generation, start-up and contingency reserves for 1000 power
plants with total capacity of 146,000 MW spread over 13 Midwestern states of U.S. and
Manitoba (Canada) owned by 750 companies supplying 40 million users, resulting in savings
of $2 billion over the period 2007–2010.
 2010: Mexico’s central security depository, INDEVAL, used linear programming to develop a
secure and automatic clearing and settlement engine to determine the set of transactions that
can be settled to maximize the number of traded securities, thereby efficiently processing
transactions averaging $250 billion daily and optimally using available cash and security
balances.
 2009: Hewlett-Packard developed an efficient frontier analysis based Revenue Coverage
Optimization tool for analysis of its order history to manage product variety, thereby enabling
increased operational focus on most critical products, making data-driven decisions and
increasing its market share, customer satisfaction, and profits by more than $500 million since
2005.

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 2008: Netherlands Railways developed a constraint programming based railway timetable for
scheduling about 5,500 trains daily, while ensuring maximum utilization of railway network,
improving the robustness of the timetable, and optimal utilization of rolling stock and crew
thereby resulting in additional annual profit of €40 million.
 2005: Motorola used mixed integer programming to develop Internet-enabled supplier
negotiation software with flexible bidding formats, multistage negotiation capabilities, multiple
online negotiation formats (with reverse e-auction, online competitive bidding facilities), and
optimized selection of vendors to support its global procurement function, automated
negotiations, and the management of a heterogeneous supply base of more than thousand
vendors with different product portfolios and delivery capabilities, thereby resulting in savings
of more than $600 million.

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 OR Applications in Business:
Many of the scientists who had participated on OR teams or who had heard about this work
were motivated to pursue research relevant to the field; important advancements in the state of the art
resulted. A prime example is the simplex method for solving linear programming problems. Many of
the standard tools of OR, such as linear programming, dynamic programming, queuing theory, and
inventory theory, were relatively well developed before the end of the 1950s. The development of
electronic digital computers, with their ability to perform arithmetic calculations thousands or even
millions of times faster than a human being can, was a tremendous boon to OR. Today, literally
millions of individuals have ready access to OR software. Consequently, a whole range of computers
from mainframes to laptops now are being routinely used to solve OR problems.
• Linear Programming: Linear Programming (LP) is a mathematical technique of assigning a fixed
amount of resources to satisfy a number of demands in such a way that some objective is optimized
and other defined conditions are also satisfied.
• Transportation Problem: The transportation problem is a special type of linear programming
problem, where the objective is to minimize the cost of distributing a product from a number of
sources to a number of destinations.
• Assignment Problem: Succinctly, when the problem involves the allocation of n different facilities
to n different tasks, it is often termed as an assignment problem.
• Queuing Theory: The queuing problem is identified by the presence of a group of customers who
arrive randomly to receive some service.
• Game Theory: It is used for decision making under conflicting situations where there are one or
more opponents (i.e., players). In the game theory, we consider two or more persons with different
objectives, each of whose actions influence the outcomes of the game.
• Goal Programming: It is a powerful tool to tackle multiple and incompatible goals of an enterprise.
• Simulation: It is a technique that involves setting up a model of real situation and then performing
experiments. Simulation is used where it is very risky, cumbersome, or time consuming to conduct real
study or experiment to know more about a situation.

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• Nonlinear Programming: These methods may be used when either the objective function or some
of the constraints are not linear in nature.
• Integer Programming: These methods may be used when one or more of the variables can take only
integral values. Examples are the number of trucks in a fleet, the number of generators in a power
house, etc.
• Dynamic Programming: Dynamic programming is a methodology useful for solving problems that
involve taking decisions over several stages in a sequence.
• Network Scheduling: PERT and CPM. Network scheduling is a technique used for planning,
scheduling and monitoring large projects. Such large projects are very common in the field of
construction, maintenance, computer system installation, research and development design, etc.
OPERATION RESEARCH MODEL

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 Phases of Operations Research Study:
Seven Steps of OR Study, An OR project can be split in the following seven steps:
Step 1: Formulate the problem The OR analyst first defines the organization’s problem. This
includes specifying the organization’s objectives and the parts of the organization (or system) that
must be studied before the problem can be solved.
Step 2: Observe the system Next, the OR analyst collects data to estimate the values of the
parameters that affect the organization’s problem. These estimates are used to develop (in Step 3) and
to evaluate (in Step 4) a mathematical model of the organization’s problem.
Step 3: Formulate a mathematical model of the problem The OR analyst develops an idealized
representation — i.e. a mathematical model — Of the problem.
Step 4: Verify the model and use it for prediction The OR analyst tries to determine if the
mathematical model developed in Step 3 is an accurate representation of the reality. The verification
typically includes observing the system to check if the parameters are correct. If the model does not
represent the reality well enough then the OR analyst goes back either to Step 3 or Step 2.
Step 5: Select a suitable alternative Given a model and a set of alternatives, the analyst now
chooses the alternative that best meets the organization’s objectives. Sometimes there are many best
alternatives, in which case the OR analyst should present them all to the organization’s decision-
makers, or ask for more objectives or restrictions.
Step 6: Present the results and conclusions The OR analyst presents the model and
recommendations from Step 5 to the organization’s decision-makers. At this point the OR analyst may
find that the decision makers do not approve of the recommendations. This may result from incorrect
definition of the organization’s problems or decision-makers may disagree with the parameters or the
mathematical model. The OR analyst goes back to Step 1, Step 2, or Step 3, depending on where the
disagreement lies.
Step 7: Implement and evaluate recommendation Finally, when the organization has accepted
the study, the OR analyst helps in implementing the recommendations. The system must be constantly

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monitored and updated dynamically as the environment changes. This means going back to Step 1,
Step 2, or Step 3, from time to time.
In this course we shall concentrate on Step 3 and Step 5, i.e., we shall concentrate on
mathematical modeling and finding the optimum of a mathematical model. We will completely omit
the in-between Step 4. That step belongs to the realm of statistics. The reason for this omission is
obvious: The statistics needed in OR is way too important to be included as side notes in this course!
So, any OR’ist worth her/his salt should study statistics, at least up-to the level of parameter
estimization.

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 Features of Operation Research:
The significant features of operations research include the followings:
Decision-making: Every industrial organisation f aces multifacet problems to identify best possible
solution to their problems. OR aims to help the executives to obtain optimal solution with the use of
OR techniques. It also helps the decision maker to improve his creative and judicious capabilities,
analyse and understand the problem situation leading to better control, better co-ordination, better
systems and finally better decisions.
Scientific Approach: OR applies scientific methods, techniques and tools for the purpose of analysis
and solution of the complex problems. In this approach there is no place for guess work and the person
bias of the decision maker.
Inter-disciplinary Team Approach: Basically the industrial problems are of complex nature and
therefore require a team effort to handle it. This team comprises of scientist/mathematician and
technocrates. Who jointly use the OR tools to obtain a optimal solution of the problem. The tries to
analyse the cause and effect relationship between various parameters of the problem and evaluates the
outcome of various alternative strategies.
System Approach: The main aim of the system approach is to trace for each proposal all significant
and indirect effects on all sub-system on a system and to evaluate each action in terms of effects for
the system as a whole. The interrelationship and interaction of each sub-system can be handled with
the help of mathematical/analytical models of OR to obtain acceptable solution.
Use of Computers: The models of OR need lot of computation and therefore, the use of computers
becomes necessary. With the use of computers it is possible to handle complex problems requiring
large amount of calculations.
The objective of the operations research models is to attempt and to locate best or optimal
solution under the specified conditions. For the above purpose, it is necessary that a measure of
effectiveness has to be defined which must be based on the goals of the organisation. These measures
can be used to compare the alternative courses of action taken during the analysis.

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 SCOPE OF OPERATIONS RESEARCH:
As presented in the earlier paragraphs, the scope of OR is not only confined to any specific
agency like defence services but today it is widely used in all industrial organisations. It can be used to
find the best solution to any problem be it simple or complex. It is useful in every field of human
activities, where optimisation of resources is required in the best way. Thus, it attempts to resolve the
conflicts of interest among the components of organization in a way that is best for the organisation as
a whole. The main fields where OR is extensively used are given below, however, this list is not
exhaustive but only illustrative.
National Planning and Budgeting OR is used for the preparation of Five Year Plans, annual budgets,
forecasting of income and expenditure, scheduling of major projects of national importance, estimation
of GNP, GDP, population, employment and generation of agriculture yields etc.
Defence Services Basically formulation of OR started from USA army, so it has wide application in
the areas such as: development of new technology, optimization of cost and time, tender evaluation,
setting and layouts of defence projects, assessment of “Threat analysis”, strategy of battle, effective
maintenance and replacement of equipment, inventory control, transportation and supply depots etc.
Industrial Establishment and Private Sector Units OR can be effectively used in plant location and
setting finance planning, product and process planning, facility planning and construction, production
planning and control, purchasing, maintenance management and personnel management etc. to name a
few.
R & D and Engineering Research and development being the heart of technological growth, OR has
wide scope for and can be applied in technology forecasting and evaluation, technology and project
management, preparation of tender and negotiation, value engineering, work/method study and so on.
Business Management and Competition OR can help in taking business decisions under risk and
uncertainty, capital investment and returns, business strategy formation, optimum advertisement
outlay, optimum sales force and their distribution, market survey and analysis and market research
techniques etc.
Agriculture and Irrigation In the area of agriculture and irrigation also OR can be useful for project
management, construction of major dams at minimum cost, optimum allocation of supply and
collection points for fertilizer/seeds and agriculture outputs and optimum mix of fertilizers for better
yield.

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Education and Training OR can be used for obtaining optimum number of schools with their
locations, optimum mix of students/teacher student ratio, optimum financial outlay and other relevant
information in training of graduates to meet out the national requirements.
Transportation Transportation models of OR can be applied to real life problems to forecast public
transport requirements, optimum routing, forecasting of income and expenses, project management for
railways, railway network distribution, etc. In the same way it can be useful in the field of
communication.
Home Management and Budgeting OR can be effectively used for control of expenses to maximize
savings, time management, work study methods for all related works. Investment of surplus budget,
appropriate insurance of life and properties and estimate of depreciation and optimum premium of
insurance etc.
The Operation Research Approach

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 SIMPLIFICATION OF OR MODELS:
The more complex, expensive and large in scale the designed system is, the less allowable in it
are wilful decisions and the more gain in importance scientific methods which, when implemented,
provide an estimate of each decision’s consequences, help discard the unallowable versions and
recommend the most successful ones. They help in assessing whether the available information is
adequate to prepare a correct decision and, if not, then indicate what data should be additionally
collected. It would be extremely risky to be guided solely by intuition i.e., experience and common
sense. Modern science and technology evolve so fast that the experience may simply not have been
acquired. The calculations that make the process of decision-making easier are the subject matter of
operations research.
Under the complex situations some of the models need a lot of computational efforts
particularly in case of linear programming. Efforts should be made to simplify the situation and
development of model so as to generate the optimal solution with minimum effort. The selection of
model for a particular problem has its own bearings and availability of solution. Assumptions to be
imposed on the model should be such that, it makes it possible to achieve desirable solution without
affecting the constraints of the problem. In most intricate cases, when scanning an operation and its
outcome depend on a large number of intimately interrelated random factors, the analytical techniques
fail altogether and the analyst has to employ Monto Carlo methods of statistical modelling. In this case
a computer simulates the process of an operation development with all the random variables involved.
This manipulation of the process yields an observation of one random operation run. One such
realization gives no grounds for decision-making, but, once a manifold of them is collected after
several runs, it may be handled statistically to find the process means and make inferences about the
real system and how in the mean, it is influenced by initial conditions and controllable variables. Both
analytical and statistical models are widely implemented in OR. Each of the models possesses its own
advantages and disadvantages. The analytical models are rougher, but they yield more meaningful
results. However, statistical models are more accurate, but are bulky, poorly analysable, need more
computational time and do not yield optimal results. Therefore, the analyst should make correct
judgement to select either model depending upon requirements and situation of the problem.

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 LIMITATIONS OF OPERATIONS RESEARCH:
OR has some limitations however, these are related to the problem of model building and the
time and money factors involved in application rather than its practical utility. Some of them are as
follows:
Magnitude of Computation: Operations research models try to find out optimal solution taking into
account all the factors. These factors are enormous and expressing them in quantity and establishing
relationships among these require voluminous calculations which can be handled by computers.
Non-Quantifiable Factors: OR provides solution only when all elements related to a problem can be
quantified. All relevant variables do not lend themselves to quantification. Factors which cannot be
quantified find no place in OR study. Models in OR do not take into account qualitative factors or
emotional factors which may be quite important.
Distance between User and Analyst: OR being specialist’s job requires a mathematician or
statistician, who might not be aware of the business problems. Similarly, a manager fails to understand
the complex working of OR. Thus there is a gap between the two. Management itself may offer a lot of
resistance due to conventional thinking.
Time and Money Costs: When basic data are subjected to frequent changes, incorporating them into
the OR models is a costly proposition. Moreover, a fairly good solution at present may be more
desirable than a perfect OR solution available after sometime. The computational time increases
depending upon the size of the problem and accuracy of results desired.
Implementation: Implementation of any decision is a delicate task. It must take into account the
complexities of human relations and behaviour. Sometimes, resistance is offered due to psychological
factors which may not have any bearing on the problem as well as its solution.

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 Conclusion:
Operations research is the discipline of applying advanced analytical methods to help make
better decisions. OR is the use of advanced analytical techniques to improve decision making.
Mathematical programming is the OR technique that has been most widely applied in business
organizations. Mathematical programming has been used to solve a considerable range of problems in
business organizations - forming portfolios of equities, employee oriented, customer oriented product
oriented and production oriented etc. Today’s global markets and instant communications mean that
customers expect high-quality products and services when they need them, where they need them.
Organizations, whether public or private, need to provide these products and services as effectively
and efficiently as possible by the OR techniques at all.
Bibliography:
www.google.com
www.wikipedia.com
www.bbusinessjagrons.com
www.investopedia.com